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Numerical simulations of three-dimensional nonlinear free surface flows. (English) Zbl 0698.76009

Computational engineering with boundary elements. Vol. 1: Fluid and potential problems, Proc. 5th Int. Conf. Boundary Elem. Technol., Newark/DE (USA) 1990, 47-60 (1990).
Summary: [For the entire collection see Zbl 0695.00027.]
Based on the boundary element method, a numerical algorithm is developed to simulate transient nonlinear free surface motions. The fluid is assumed to be inviscid, incompressible, and the flow irrotational. The nonlinear free surface boundary conditions are treated by using an Eulerian-Lagrangian scheme where the position and the potential of the free surface at an advanced time-step is given by the Taylor series expansions in terms of a small time-step size. This method allows precise control over numerical accuracy by judicious selection of the appropriate number of terms in the series. The boundary value problems for the velocity potential and its Lagrangian time derivatives are converted poential and its Lagrangian time derivatives are converted into integral equations which are then solved numerically. Linear triangular elements are used for numerical integrations over the bounding surfaces of the flow domain. The representation of the free surface geometry and computations of tangential derivatives are performed using B-splines. Several numerical examples, concerning gravity wave generations and propagations, are presented.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0695.00027